\documentclass{article}
\usepackage{amsmath}
\title{Linear program formulation of parametrized cut function}
\begin{document}
\maketitle
We consider $f(T)$ as a graph in cut function. If only $\min_{t\in T} f(T)$ is considered, this is the problem of maxflow version. If we allow some linear terms to be subtracted, we can still solve the problem. In this article, we will use the LP formulation to interprete the problem.
\begin{align}
\tilde{h}(T) &= f(T) - y(T)\\
\tilde{h}& = \min_{t \in T \subseteq V} \tilde{h}(T) \label{eq:pmq}
\end{align}
where
$y(T) = \sum_{i \in T} y_i$.  WLOG, we assume $y_t = 0$.


\end{document}

